Reflected resistance calculation: A transformer has 50 primary turns and 10 secondary turns. If the secondary load is 250 Ω, what resistance is reflected to the primary side?

Introduction / Context:
Impedance reflection across ideal transformers is foundational for matching stages. When given explicit turn counts, you can compute the exact reflected resistance to the primary to analyze source loading and power transfer.

Given Data / Assumptions:

• Np = 50 turns, Ns = 10 turns.
• RL(sec) = 250 Ω.
• Ideal transformer; R_ref(primary) = RL * (Np/Ns)^2.

Concept / Approach:
The impedance seen at the primary equals the secondary load multiplied by the square of the turns ratio from primary to secondary. A higher Np/Ns makes the primary appear more heavily loaded (higher reflected resistance).

Step-by-Step Solution:
Np/Ns = 50/10 = 5R_ref = RL * (Np/Ns)^2R_ref = 250 * 5^2 = 250 * 25R_ref = 6,250 Ω

Verification / Alternative check:
If this transformer were used to step voltage down by 5, it would step impedance up by 25 from the primary perspective; 250 Ω * 25 = 6,250 Ω matches the calculation.

Why Other Options Are Wrong:

• 250 Ω: The actual secondary load, not the reflected primary value.
• 25 Ω: Would come from inverting the ratio incorrectly.
• 62,500 Ω: Off by 10x due to a powers-of-ten slip.

Common Pitfalls:
Forgetting the square on the turns ratio or swapping Ns and Np in the formula, which yields a drastically different value.

Final Answer:
6,250 Ω